[vvelez]

Sea \( \Omega \subseteq{\mathbb{R}^{n}} \). Si \( f\in{L^{1}_{loc}(\Omega)} \) y \( \displaystyle\int_{\Omega}f\cdot{\phi}\;dx=0 \) \( \forall{\phi}\in{C_{c}^{\infty}(\Omega)} \) entonces \( f=0 \)

[Luis Fuentes]

Hola

Sea \( \Omega \subseteq{\mathbb{R}^{n}} \). Si \( f\in{L^{1}_{loc}(\Omega)} \) y \( \displaystyle\int_{\Omega}f\cdot{\phi}\;dx=0 \) \( \forall{\phi}\in{C_{c}^{\infty}(\Omega)} \) entonces \( f=0 \)

Mira por aquí:

https://math.stackexchange.com/questions/2008155/proving-that-locally-integrable-functions-are-embedded-in-the-space-of-distribut

Saludos.

[vvelez]

Michas gracias!!